I wouldn't bother with the Statue of Liberty. It's really not all that impressive, and the lines are way too long, especially on a nice day.
Central Park is great, and worth seeing. If you like animals, you can hit two birds with one stone (figuratively) and do the Central Park Zoo at the same time. Central Park South area hsa the most interesting shops. Grand Central Station is also still neat, especially at the busy times (morning rush/lunch/evening rush), since you never know what you'll see. If you were there on election day back in 2000, you would have seen some high school students performing a wedding, which I... umm... may or may not have been involved with.
Times Square is probably good to see at some point in your life, although really the main thing to do there is spend money.
Go and see the site where the World Trade Center used to be. I always take friends and do my best to explain what was there that we all lost.
ABSOLUTELY do a tour by air if you can. I think perhaps the most spectacular thing is to see NYC by air. Plus, then you can see the Statue of Liberty from a much better angle and get better pictures. Give Danos a hollar on this, I seem to recall he does this frequently, and is a great guy to hang out with anyway. I've done it with a friend before, but never as PIC. I also flew the Aztec over the NY Bravo at 7500 a few weeks back, which was great fun, but would've been much better to be at a lower altitude.
If you can, make it to Brooklyn for food (and cheesecake!) at Junior's.
The subway is efficient (and gives you a real taste of NYC), but really the best way to get around NYC is motorcycle, and what I try to do. If you're going to use public transit, the bus is slower, but then you can look out the window and see much more of what there is. A "Fun Pass" MetroCard gives you unlimited on and off the bus/subway for one day. You'll need one for each of you, but definitely worthwhile.
If I happen to be around, let me know and I'd be glad to give you a tour, and even provide the vehicular transport. Just let me know when you're coming in.